Competition between Icosahedral Motifs in AgCu, AgNi, and AgCo

Article pubs.acs.org/JPCC

Competition between Icosahedral Motifs in AgCu, AgNi, and AgCo Nanoalloys: A Combined Atomistic−DFT Study Kari Laasonen,† Emanuele Panizon,‡ Davide Bochicchio,‡ and Riccardo Ferrando*,‡ †

School of Chemical Technology and COMP Center of Excellence, Aalto University, P.O. Box 16100, FI-00076 Espoo, Finland Dipartimento di Fisica, dell'Università di Genova and IMEM/CNR, Via Dodecaneso 33, Genova I16146, Italy

‡

ABSTRACT: The structures of AgCu, AgNi, and AgCo nanoalloys with icosahedral geometry have been computationally studied by a combination of atomistic and density-functional theory (DFT) calculations, for sizes up to about 1400 atoms. These nanoalloys preferentially assume core−shell chemical ordering, with Ag in the shell. These core−shell nanoparticles can have either centered or off-center cores; they can have an atomic vacancy in their central site or present different arrangements of the Ag shell. Here we compare these different icosahedral motifs and determine the factors influencing their stability by means of a local strain analysis. The calculations find that off-center cores are favorable for sufficiently large core sizes and that the central vacancy is favorable in pure Ag clusters but not in binary clusters with cores of small size. A quite good agreement between atomistic and DFT calculations is found in most cases, with some discrepancy only for pentakis-dodecahedral structures. Our results support the accuracy of the atomistic model. Spin structure and charge transfer in the nanoparticles are also analyzed.

1. INTRODUCTION In recent years there has been increasing interest toward bimetallic nanoparticles because of their potential applications to magnetism, catalysis, and optics.1 These nanoparticles, often called nanoalloys, present properties with a high degree of tunability, which is a consequence of the great variety of morphologies that they can present. The morphology of a nanoalloy is specified by its geometric structure, which can be crystalline or noncrystalline, and by its chemical ordering, which is the pattern in which the different atomic elements are arranged within the geometric structure. When the components of the nanoparticle are weakly miscible, as in the case of AgCu, AgNi, and AgCo, the core− shell chemical ordering is often expected. In core−shell nanoalloys, an external shell of the less cohesive element (in these cases Ag) covers a core of the more cohesive element M (M being either Cu, Ni, or Co). The interest in core−shell AgM nanoalloys has been stimulated by their optical properties2,3 because of the sharp surface plasmon resonance of Ag. The surface plasmon peak frequency can be shifted by changing chemical ordering.2 AgCu and AgNi have also interesting magneto-optical properties. The magnetic and optical properties of core−shell nanoparticles strongly depend on the shape and placement of the cores.2,4 Applications to catalysis are also possible, such as in the oxygen reduction reaction for AgCo and AgCu.5,6 AgCu nanoalloys are proposed for fabricating low-temperature Pb-free solders.7 In recent times, the advances in techniques such as scanning electron transmission microscopy (STEM) with Z-contrast imaging8 and energy-filtered TEM9 have allowed to reveal the © XXXX American Chemical Society

internal structures of binary nanoparticles. Theoretically determining shape and placement of the cores for cluster sizes (3−4 nm of diameter) that are more easily accessible to this kind of experiments is therefore of great importance. Core−shell arrangements of AgM nanoparticles have been found in many experiments and calculations.3,6,10−35 For nanoparticle sizes up to about 103 atoms, global optimization studies indicate that core−shell icosahedra (Ih) are among the most stable morphologies.24 The stabilization is due to the strain release effect that is achieved by cores made of smaller atoms than the shell atoms.36 In fact, in single-component clusters, the icosahedron is strongly compressed at its center. Within the icosahedral motif, several different structures have been proposed in recent years. Besides the classical Mackay icosahedron,37 icosahedra with anti-Mackay outer shell38 and chiral icosahedra have been found for Ag-poor compositions.24 Moreover, there are icosahedral structures which achieve strain release by different mechanisms. For example, it has been demonstrated by means of atomistic calculations in pure clusters that icosahedra with a central atomic vacancy are more stable than icosahedra without the vacancy.39 Icosahedral structures with a central vacancy have been also proposed for the thiolate-protected gold cluster Au144(SR)60.40 Recently, a transition from icosahedra with a centered core to icosahedra with an off-center core has been found depending on the nanoalloy composition,34 for systems such as AgCu, AgNi, Received: October 20, 2013 Revised: November 19, 2013

A

dx.doi.org/10.1021/jp410379u | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

shell structures is the following. In an AgM cluster, to each Ag atom i is given a weight wAg(i)

AgCo, and AuCo. These results were obtained by atomistic modeling using semiempirical interaction potentials, without being checked at a higher theory level such as DFT. In this paper we compare the energetic stability of the different types of icosahedra. We consider core−shell AgM nanoalloys with centered or off-center cores and with or without central vacancies. We also discuss the stability of a new type of core−shell cluster with icosahedral symmetry, the pentakis-dodecahedron.41 We perform the cluster energy calculations by means of both atomistic and higher-level calculations. The latter, based on DFT, take explicitly into account the electronic structure of the nanoparticles. The DFT calculations are important also for the following reasons. First, they allow us to assess the validity of the atomistic models that have been used in finding the different types of icosahedra. Atomistic models are in fact extremely useful when dealing with nanoparticles of several hundred or even thousand atoms, where the DFT calculations are very cumbersome and therefore limited to evaluate a small number of structures. However, the accuracy of atomistic models is often questionable, so that their assessment by higher-level calculations is important. Second, the DFT calculations give insight into the magnetic properties of the nanoparticles and to charge transfer phenomena, which are not accessible by modeling at the atomistic level.

wAg(i) = [nM(i) + 1]2

where nM(i) is the number of M nearest neighbors of atom i. The weight given to an M atom depends on whether it stays at the nanoparticle surface or inside the nanoparticle. For M atoms inside the nanoparticle wM(i) = [nAg (i) + 1]2

∑ j , rij ≤ rc

Aij e−pij (rij / r0ij − 1) −

∑ j , rij ≤ rc

(3)

where nAg(i) is the number of Ag nearest neighbors of atom i. For M atoms at the surface wM(i) = [nAg (i) + 1 + 12 − nAg (i) − nM(i)]2

(4)

as if the missing neighbors were Ag atoms. Usually tailored exchanges allows finding chemical ordering arrangements with lower energy than random exchanges. Random exchanges are rather poorly efficient when dealing with the nanoparticle sizes and compositions considered in this work. It has been checked, however, that at smaller size both random and tailored exchanges lead to the same results, the latter being faster in reaching the lowest-energy structures. For each size and composition, at least five independent simulations of 105 steps each have been made. Local Stress Calculations. In the following we will calculate the local stress tensor σi on each atom i, whose components are defined as48

2. MODEL AND METHODS 2.1. Atomistic Calculations. Interaction Potential. The interactions are described by an atomistic model developed within the second-moment approximation to the tight-binding model (SMATB potential), known also as Gupta or RGL potential.42−44 In this model, the potential energy of the system depends on the relative distances between atoms rij, and it is written as the sum of single-atom contributions Ei: Ei =

(2)

σiab =

1 Vi

∑ j≠i

a b ∂Ei rij rij ∂rij rij

raij

(5)

rbij

In this equation, and (with a, b = x, y, z) are the Cartesian components of the vector rij and rij is its modulus. Vi is the atomic volume. The isotropic atomic pressure Pi is related to the trace of σi as follows: 1 Pi = − Tr(σi) 3

ξij 2e−2qij(rij / r0ij − 1) (1)

(6)

In the following we will also make use of another invariant of the stress tensor, the quantity τi defined as

The parameters pij, qij, Aij, ξij, and r0ij depend indeed on the atomic species of the pair ij only. As for r0ij, we take the equilibrium distances in the bulk crystals at zero temperature for Ag−Ag and M−M pairs and the average of the two for Ag− M pairs. rc is an appropriate cutoff distance. In this work we choose to put rc equal to the second-neighbor distance in the respective bulk solids for Ag−Ag and M−M pairs. The potential is then linked to zero at the third-neighbor distance by a polynomial function in such a way that the resulting function is continuous with continuous derivatives. For Ag−M pairs, the cutoff is between the second neighbors of Ag and the third neighbors of M. The parameters of the potential can be found in refs 11 and 45 for AgCu and AgNi and in ref 46 for AgCo. Global Optimization Searches. The lowest energy structures are searched for by a basin-hopping procedure47 with exchange moves only. In an exchange move, the positions of two atoms of different species are swapped. The move is followed by local relaxation to reach the closest local minimum. Both random and tailored exchanges are used.24 In tailored exchanges, atoms are chosen with different probabilities according to their local environment. An effective scheme for weighing probabilities in systems with tendency to form core−

τi =

1 (σixx − σi yy)2 + (σi yy − σizz)2 + (σizz − σixx)2 3 (7)

τi measures the anisotropy of the local stress, with τi = 0 corresponding to the perfectly isotropic case. 2.2. Density Functional Theory Calculations. The ab initio density functional theory (DFT) based calculations have been done with the CP2K software package and with the QUICKSTEP49,50 module using the GPW method51 where the atom-centered Gaussian basis sets are used together with augmented plane wave basis sets. For the DFT force calculations the PBE52 and BLYP53 functionals were used and the DZVP-MOLOPT-SR basis set together with GTH pseudopotential for all atoms.54 Few tests were done with the dispersion-corrected BLYP-D3 functional. The model proposed by Grimme et al. was used.55 For all atoms a pseudopotential with most electrons were used. For Ag and Cu 11 electron, Co 17 and Ni 18 electron pseudopotentials were used. The plane wave kinetic energy cutoff was set to 800 Ry (except for the largest clusters, where the value of 700 Ry was used). To improve the stability of the calculations, the clusters were B



Article

treated with periodic boundary conditions. A cubic cell with 30 Å side length was used for most of the clusters. The 560-atom clusters were computed with 38 Å cell and the 1415-atom clusters with 40 Å cell. The spin of the system was treated with the spin density version of the PBE and BLYP functionals. The total spin of the clusters was roughly optimized. Few values of the total spin were tried around the minima, and the total spin corresponding to the lowest energy was used. The energy differences were not sensitive to the total spin. All calculations were started with the atomistic potential optimized geometries. These geometries were optimized with DFT. The accuracy of the minima was a few 0.1 eV, which is enough when compared to the empirical potentials. We tested the BLYP-D3 functional for hole/no hole energy difference for Ag560, Ag506Ni54, and Ag414Ni146 clusters. The results were with 0.2 eV from the BLYP results. Some tests with the GPAW56,57 code have been also made for the icosahedra with and without central vacancy (see section 3.2). The largest Co containing cluster (Ag1106Co309) was difficult to compute, and the minimum spin search was not done. These results are not included in the tables. Figure 1. Structure of icosahedral AgNi nanoparticles of 561 atoms and composition Ag414Ni147, corresponding to a total number of shells n = 6 and to a core of k = 4 shells. In this case kc = 3, so that the lowest energy configuration of the core is off-center and of low symmetry. Each cluster is shown in two views. Top row: cluster with centered symmetric core. Bottom row: off-center core. In (c) a local distortion of the shell covering the off-center core is visible. In (b) and (d) Ag atoms are shown as small spheres so that the Ni core is visible.

3. RESULTS 3.1. Icosahedra with Centered and Off-Center Cores. It has been shown recently by global optimization searches within the SMATB model that the shape and position of the core in core−shell Mackay icosahedra depend on composition.34 Let us consider an icosahedron of n concentric atomic layers in total, with a number of core atoms corresponding to to the inner k concentric layers. The atomistic calculations show that there is a critical value of k, referred to as kc, for which a morphological instability of the core starts to develop. For k < kc the core is centered and symmetric; for k ≥ kc the core extends toward the nanoparticle surface and becomes much less symmetric (see Figure 1). In the following we consider icosahedra of sizes 561 and 1415, with compositions Ag414M147 and Ag1106M309, where M is Cu, Ni, or Co. In ref 34 it has been shown by SMATB calculations that in these nanoparticles off-center low-symmetry cores are energetically favorable. This was attributed to the presence of atomic sites with negative local pressure in the cores with k ≥ kc. In these sites, substituting M atoms with Ag atoms is favorable because Ag atoms have a larger size. We can analyze strain release in more details by considering, besides the local average pressure Pi as in ref 34, the complete local strain tensor σi and its anisotropy invariant τi, as defined in eqs 5−7. These quantities are calculated by the atomistic potential. The pressure maps of Figure 2 show that the atoms of the outer concentric layer of symmetric cores have a strongly negative pressure, indicating a strong tensile strain. For the nanoparticle of size 1415, the negative pressure extends also to inner parts of the core. Moreover, the atoms of the inmost concentric layer of the shell present a significantly positive pressure. This shows that the atoms on the two sides of the core−shell interface present a large pressure difference. The analysis of the anisotropy of pressure (see Figure 3) indicates a strong anisotropy for the Ag atoms at the interface. By diagonalizing the strain tensor on each atom, it is possible to separate with good approximation a radial and a tangential contribution to the strain and therefore to the pressure. This reveals that these Ag atoms feel a notable compressive tangential strain, whereas the radial component is small. This behavior is due to the radial contraction of the Ag atoms to

adapt to the small Ni core, which causes a tangential compression of these Ag atoms. The comparison of the pressure maps of Figure 2 for icosahedra with centered symmetric and off-center cores show a general strain relaxation in the latter, with most Pi close to zero. This is quantitatively demonstrated by the data in Table 1, where we report the difference ΔP between maximum and minimum pressure (Pmin and Pmax i i , respectively) and the average deviation from zero pressure |P| = (1/N)∑i|Pi| for the different nanoparticles. The stability of centered and off-center cores is determined by competing factors. Off-center cores present a much better strain release if the core is sufficiently large. However, in offcenter cores there are fewer M−M bonds and more Ag−M bonds than in centered cores. This has an energetic cost because M−M bonds are stronger. This energetic cost is compensated by two effects. The first effect is a much better strain release. The second effect is the advantage of putting a considerable number of M atoms in subsurface positions, which are quite favorable in these systems.11 Our calculations, however, show that these effects indeed overcompensate for the loss of M−M bonds in favor of Ag−M bonds when the core is sufficiently large. The comparison of the SMATB energy differences with DFT ones is reported in Table 2. The DFT calculations confirm the stronger energetic stability of off-center low-symmetry cores, at both the PBE and BLYP level, in good agreement with the SMATB results. At size 561, quantitative agreement between DFT and SMATB is quite good for AgCu and AgNi, while for AgCo SMATB calculations overestimate the difference between the centered and the off-center core structures. It should however noted that at the DFT level there might be other lowsymmetry isomers of even lower energy. Unfortunately, a C



Article

atom in single-element clusters is so compressed that its removal can be energetically favorable, as it was demonstrated by SMATB calculations by Mottet et al.39 In the following we first check this result at the DFT level for pure Ag icosahedra, and then we consider the energetic stability of the central vacancy in binary Ag−M nanoparticles. The results of both SMATB and DFT calculations for icosahedra of 560 atoms are reported in Table 3. Let us consider the pure Ag560 cluster. We perform global optimization searches of the most stable icosahedral isomers within the SMATB model, finding the icosahedron with the central atomic vacancy as the lowest-energy isomer. The best isomer with no central vacancy has one vertex missing on its surface (see Figure 4). The structure with the vacancy has fewer nearest-neighbor bonds, which are however compensated by a better strain release.39 In fact, the structure with no vacancy is 0.44 eV higher than the structure with the vacancy, a result that is confirmed also by the DFT calculations both at the PBE and at the BLYP level, however, with smaller energy differences (0.24 and 0.26 eV, respectively). In binary clusters, the scenario is different. If we put an M core of 54 atoms and compare the results for the same geometric structures considered for the pure Ag cases (see Figure 4), we find that the central vacancy is never favored, neither by SMATB nor by DFT calculations. As shown in Table 3, energy differences are of the order of 1 eV in favor of the structure without vacancy. The trend is the same also for an M core of 146 atoms, even though the energy differences are somewhat smaller for AgCu. What is the cause of this behavior? If we consider the local pressure on the central atom in the pure Ag560 cluster, we find by SMATB calculations that it is of about 32 GPa. On the other hand, in binary nanoparticles this pressure decreases for example to about 13 GPa in Ag506Cu54 and to 17 GPa in Ag414Cu146. Therefore, the strain release associated with the creation of the central vacancy is smaller in binary nanoparticles, so that it is not sufficient anymore to compensate the decreased number of nearest-neighbor bonds. These results thus indicate that the central vacancy is not energetically favorable in Ag−M icosahedral nanoparticles with centered cores. On the other hand, our global optimization simulations do not find evidence of central vacancies also in the case of offcenter low-symmetry cores. Central vacancies may become favorable again when the Ag shell becomes very thin. In this case M cores can be centered and symmetric, while the Ag shell can assume different arrangements than those of the Mackay icosahedron, such as the anti-Mackay icosahedron, the chiral icosahedron,24 and the pentakis-dodecahedron (see section 3.3). The comparison of SMATB and DFT data in Table 3 shows again a good agreement between these calculations, thus supporting the validity of the SMATB model. As stated in section 2.2, these clusters have been chosen for checking the DFT results against the choice of the basis set. Indeed, the CP2K has very limited basis sets for the studied metals. It has only SZV-MOLOPT-SR-GTH and DZVPMOLOPT-SR-GTH. Some tests with the smaller basis set have been done, and much larger energy differences were obtained. The sign never changed. We also did comparisons with the GPAW code.56,57 This code uses grids as basis set and is insensitive to basis set superposition type errors. Unfortunately, the magnetic clusters were very difficult to get converged so we only tested the Ag560 and Ag506Cu54 clusters.

Figure 2. Cross sections of AgNi icosahedra with centered symmetric and off-center low-symmetry cores. In the left column we show the arrangement of the atomic species, drawing them with different colors (gray for Ag and red for Ni). In the right column we show the corresponding local pressure maps, according to the SMATB calculations. Negative, zero, and positive pressures correspond to blue, green, and red atoms, respectively. (a1) and (a2): Ag414Ni147 with centered symmetric core. (b1) and (b2): Ag414Ni147 with off-center core. (c1) and (c2): Ag1106Ni309 with centered symmetric core. (d1) and (d2): Ag1106Ni309 with off-center core. In all cases, the strain release obtained with off-center low-symmetry cores is notable.

systematic search of these isomers at the DFT level is by far too cumbersome. 3.2. Stability of Icosahedra with a Central Vacancy. Because of the peculiar geometry of the icosahedron, its central D



Article

Figure 3. (a) Map of the anisotropy parameter of pressure τi (eq 7) for Ag414Ni147 with centered symmetric core (a cross section of the cluster is shown in Figure 2a1). The atoms with strongly anisotropic pressure are marked in red and those with isotropic pressure in green. Intermediate anisotropies are marked in yellow. (b) Map of radial pressure. (c) Map of tangential pressure. In (b) and (c), negative, zero, and positive pressures are in blue, green, and red, respectively. The color scale in this figure is scaled by a factor 1/3 with respect to Figure 2. max Table 1. Minimum Pressure Pmin i , Maximum Pressure Pi , max min ΔP = Pi − Pi , and Average Deviation from Zero Pressure |P| = (1/N)∑i|Pi| for Icosahedra with Centered and Off-Center Cores According to the Atomistic Model (All Data in GPa)

cluster

core type

Pmin i

Pmax i

ΔP

|P|

Ag414Cu147 Ag414Cu147 Ag414Ni147 Ag414Ni147 Ag414Co147 Ag414Co147 Ag1106Cu309 Ag1106Cu309 Ag1106Ni309 Ag1106Ni309 Ag1106Co309 Ag1106Co309

centered off-center centered off-center centered off-center centered off-center centered off-center centered off-center

−8.61 −6.66 −13.30 −8.24 −11.89 −8.69 −10.12 −7.40 −14.87 −8.71 −12.54 −8.04

16.55 16.90 21.59 20.66 19.82 16.98 19.32 20.01 25.84 23.66 21.21 19.14

25.15 23.56 34.89 28.90 31.21 25.67 29.45 27.41 40.71 32.37 33.75 27.18

4.08 3.45 4.49 2.94 4.10 2.47 3.95 3.08 4.32 2.90 4.08 2.68

Table 3. Energy Difference ΔE = Evacancy − Enovacancy (in eV) between the Icosahedra with Central Atomic Vacancy and without Central Atomic Vacancy, According to Atomistic, DFT-PBE, and DFT-BLYP Calculationsa cluster

ΔEatom

ΔEPBE

ΔEBLYP

Ag560 Ag506Cu54 Ag506Ni54 Ag506Co54 Ag414Cu146 Ag414Ni146

−0.44 0.81 1.34 0.84 0.74 1.16

−0.24 1.26 1.85 1.82 1.01 1.90

−0.26 0.98 1.17 1.30 0.65 1.31

a Negative values of ΔE indicate that structures with central atomic vacancy are more stable.

Table 2. Energy Difference ΔE = Eoff‑center − Ecentered (in eV) between the Icosahedra with Off-Center and Centered Symmetric Cores, According to Atomistic, DFT-PBE, and DFT-BLYP Calculationsa cluster

ΔEatom

ΔEPBE

ΔEBLYP

Ag414Cu147 Ag414Ni147 Ag414Co147 Ag1106Cu309 Ag1106Ni309

−1.69 −7.08 −6.28 −4.34 −14.75

−2.68 −5.64 −1.96 −8.33 −29.12

−2.75 −4.60 −1.85 −7.37 −14.97

a Negative values of ΔE indicate that the structure with off-center core is more stable.

The energy difference between vacancy and nonvacancy clusters were −0.40 eV for Ag560 and 1.19 eV for Ag506Cu54 (with PBE GGA model). This is very close to the CP2K calculations, −0.24 and 1.26 eV (Table 3). These calculations suggest that the CP2K calculations are well converged. 3.3. Pentakis-Dodecahedral Nanoalloys. The pentakisdodecahedral nanoalloy has a core of M atoms covered by a shell of Ag atoms of monatomic thickness. The structure is shown in Figure 5a,b. The M core consists of a four-shell Mackay icosahedron covered by a further M layer of antiMackay stacking24,38 (Figure 5b). This further layer is covered by an Ag shell of monatomic thickness. The shell is arranged in 12 pentagonal patches of 16 atoms around the icosahedral

Figure 4. Structure of icosahedral AgNi nanoparticles of 560 atoms and composition Ag506Ni54. The nanoparticles have centered cores. In (a) and (b) the cluster has a central atomic vacancy, which can be seen in the cluster cross section (b). In (c) and (d) the central site is occupied by a Ni atom. Correspondingly, the Ni core misses one vertex which is now occupied by an Ag atom (as can be seen in the cross section (d)), while the external shell missed the top vertex (an Ag atom is missing at the top vertex in (c).

vertices (Figure 5a). The size of the structure is 471 or 470 atoms depending on a central atomic vacancy being present or E



Article

Table 4. Energy Difference ΔE = Epentakis − EIh (in eV) between the Pentakis-Dodecahedra and the Incomplete Icosahedral Structures According to Atomistic, DFT-PBE, and DFT-BLYP Calculationsa cluster

ΔEatom

ΔEPBE

ΔEBLYP

Ag192Cu278 Ag192Ni278 Ag192Co278

1.10 0.97 1.85

−0.65 −0.41 0.33

0.16 0.44 0.67

Negative values of ΔE indicate that pentakis-dodecahedral structures are more stable.

a

We have thus analyzed in detail the differences in atom− atom distances between the SMATB and DFT structures. In general, the differences are very small, at most a few percent. In the studied clusters there are four atom types: Ag, Cu, Ni, and Co. Of these, Ag is the dominating atom type, and it is on the outer layers of the clusters. In general, the average Ag distances in the DFT calculations are 1−2% longer than with SMATB. The only exception is found in the Ni-containing clusters, where the average Ag distances are 0.5% shorter than with SMATB. Of other metals, the Cu DFT distances are 1−2% longer than with SMATB, Co distances are within 1% (±1%) of the SMATB values, and Ni distances are 1% shorter than SMATB. The numbers above are averages over the whole cluster. If we look the distances radially in the case of Ag, the distances in the surface layers are very close to the SMATB whereas in the core layers the distances are 1−2% longer. Overall, the agreement of the SMATB and DFT distances is remarkably good. The DFT calculations give the possibility of studying the spin of the nanoparticles. We have selected a few examples of AgNi icosahedra analyzing their spin structure. In the case of Co we had convergence problems so that there are only few converged clusters. Here we consider the following cases: the pure Ni147 Mackay icosahedron; the chiral icosahedron Ag132Ni147, which is obtained from the pure Ni147 by adding a chiral Ag shell of monatomic thickness;24 Ag414Ni147 with centered symmetric and off-center cores (see Figure 2a,b); Ag192Ni278 pentakisdodecahedron (shown in Figure 5a,b for AgCo). We have first calculated the total spin of the icosahedral Ni147 cluster. Local structural relaxations has been performed starting from the ideal structure. The total spin has been optimized by means of a few calculations with fixed total spin and fitting total energy depending on the multiplicity, M, of the system (M = 2S + 1, where the S is the total spin of the system). The minimum energy has been estimated from this curve. For Ni147 the total multiplicity was ca. 101, and this correspond to M = 0.69 per atom. Radially, M presents small variations. Near the inner core of 13 atoms the multiplicity is 0.55 and in the next layers 0.70. These results can be compared to those of AgNi clusters, in which the Ni core is covered by Ag shells. It turns out that magnetization per atom is lower in all the cases. In Ag132Ni147 and Ag414Ni147, M is about 0.50 and 0.62 per Ni atom, which is lower than in the free Ni cluster. The radial structure of M is more complicated. In the case of Ag132Ni147 where Ag forms only one atomic layer on top of the Ni core, the 13 central Ni atoms have M = 0.66, the next layers have M between 0.5 and 0.6, and the outermost Ni layer has M of only 0.3. The Ag414Ni147 cluster with centered symmetric core has qualitatively similar spin structure, with M varying from 0.7 to 0.4. The decrease of magnetization with respect to pure Ni clusters is consistent with the fact that if we put a single Ni atom inside

Figure 5. Structure of icosahedral AgCo nanoparticles of 470 atoms and composition Ag192Co278. The nanoparticles have centered cores. In (a) and (b) the pentakis-dodecahedral structure is shown. In (c) and (d) the incomplete Mackay icosahedral structure is shown. In (b) and (d), Ag atoms are shown as small spheres so that the Co core is visible.

not. Corresponding compositions are Ag192M279 and Ag192M278. In the following we concentrate on the case Ag192M278. The global optimization searches within the SMATB model find that this structure is in competition with an incomplete icosahedron, made of an incomplete M core of Mackay type covered by a monatomic thickness Ag shell whose structure is to a large extent the same as in the chiral shells of ref 24. According to the SMATB model, this incomplete icosahedral structure is lower in energy than the pentakis-dodecahedral structure. Energy differences are rather small for AgNi and AgCu and larger for AgCo. At the DFT level, the stability of the pentakis-dodecahedron is enhanced compared to atomistic calculations. PBE results show in fact that the pentakis-dodecahedron becomes slightly lower in energy than the incomplete icosahedron in AgNi and AgCu, whereas for AgCo the stability of the incomplete icosahedron is confirmed, but with an even smaller energy difference. BLYP results, on the other hand, agree with atomistic calculation in predicting that the incomplete icosahedron is more stable, but by quite small energy differences. These results are therefore not completely conclusive in singling out which structure is more stable, but they all agree that the two structures should be in close competition for AgNi and AgCu, while for AgCo the preference in favor of the incomplete icosahedron is quite clear.

4. DISCUSSION The results of the previous sections have shown an overall good agreement between the energetics resulting from SMATB and DFT calculations. Here we check whether this agreement is also found on the geometric features of the clusters. In principle, local reoptimization at the DFT level may cause significant distortions in the clusters. F



Article

We have analyzed the stability of these motifs by combining atomistic and DFT calculations. Our results show that both calculations are generally in quite good agreement. The DFT calculations confirm the stronger energetic stability of off-center cores with respect to centered highly symmetric cores in Mackay icosahedra with sufficiently large cores. Both atomistic and DFT calculations indicate that central atomic vacancies are favorable in pure metal Ag icosahedra, but not in bimetallic icosahedra with small centered cores. Pentakis-dodecahedral icosahedral clusters are found to be in close energetic competition with incomplete chiral icosahedra for some specific sizes and compositions. In this case, some discrepancy between atomistic and DFT results is found. At the atomistic level, the enhanced stability of off-center cores has been rationalized by the analysis of the local stress tensor, which shows that the offcenter morphology achieves a notable strain release. For centered cores, the role of strain anisotropy at the interface between the metals has been underlined. The DFT calculations have also allowed to analyze the spin structure of AgNi clusters, showing that the inclusion of Ni in the Ag matrix decreases its magnetization. Electron transfer from Ag to Ni has been analyzed, finding results that notably depend on the method by which atomic charges are calculated. In fact, Mulliken charges show a non-negligible charge transfer, while in Bader analysis charge transfer is very small. In summary, we find that the comparison of DFT and atomistic results validates the atomistic model, confirming its reliability. This is an important point because DFT calculations are quite cumbersome for nanoparticles of the sizes treated here, so that they can be made to check the stability of a very limited number of isomers. On the contrary, atomistic calculations allow a much more thorough exploration of the energy landscape. They also allow to perform molecular dynamics simulations of cluster growth and melting on the time scales of several microsecond, thus approaching experimental time scales.

an Ag icosahedron, its magnetization is zero. Impurities dissolved in a nonmagnetic matrix can indeed become nonmagnetic.58 We note finally that in some cases DFT calculations are not able to single out the correct spin state; therefore, the results reported above are to be treated with some degree of caution. We have also analyzed the atomic charges of some of the clusters. Here we focus on two cases. First, we have analyzed Ag414Ni147 which has relatively thick Ag layer on top of the centered symmetric Ni core (Figure 1b). We analyzed the atomic charges by the Mulliken method implemented in CP2K and by the Bader method 59 implemented in the bader program60 available form University of Texas−Austin.61 These two methods give quite different values of the atomic charges. The Bader method results show small charges. For Ni, charges are from −0.07 to 0.05 e with an average of −0.015 e. For Ag, charges are from −0.07 to 0.1 e with an average of 0.0053 e. The total charge transfer (CT) of this system is of 2.2 e. No strong trends in the radial directions are observed. The Ag atoms in the outer layers are positive and in medium layers either neutral or negative. In the case of Ni only a few atoms near the center are positive, the rest being negative. The results of the Mulliken analysis do not agree with Bader analysis. First, CT is much larger. Ni charges are from −0.3 to 0.0 e with an average of −0.206 e. Ag charges are from −0.03 to 0.4 e with an average of 0.073 e. The total CT is of 30.3 e. Most of the CT is located at the Ni−Ag interface. Outside of this interface the charges are between −0.12 and 0.12 e, which are closer to the Bader case. The explanation of this discrepancy is very likely related to some hybridization of Ni and Ag basis near the interface which the Mulliken analysis misinterprets as CT. The other system that we have analyzed is the chiral icosahedron Ag132Ni147.24 This cluster has only one Ag layer on top of the Ni core (as it happens in the cluster of Figure 5b). Within Bader analysis the charges are similar to the Ag414Ni147 case. The Ni charges are from −0.07 to 0.04 e (average −0.020 e). The Ag charges are from 0.0 to 0.5 e (average of 0.023 e). The total CT is of 3.0 e. Again, the Mulliken charges are between −0.5 and 0.0 (average −0.21) for Ni and between 0.07 and 0.3 (average 0.24) for Ag. The total CT is of 31 e. As before, the largest Mulliken charges are near the Ni−Ag interface. As a check, we have also used the Lowdin population analysis,62 finding values that are rather close to the Bader charges. These results show that one needs to be very careful when analyzing the charges. In our case the Mulliken charges were large, so that drawing conclusions from them might lead to unreliable results. The Bader charges were much smaller and consistent with the assumption that there is no large CT in these metallic systems. This is consistent with the application of the SMATB model because SMATB does not contain CT terms. We would like to note that the magnetic moments of the atoms are not sensitive to the analysis. Both Bader and Mulliken analysis give similar results.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: ferrando@fisica.unige.it. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors acknowledge support from the COST Action MP0903 “Nanoalloys as Advanced Materials: From Structure to Properties and Applications”. The authors thank Prof. Tapio Ala-Nissila and Dr. Giulia Rossi for useful discussions.

■

REFERENCES

(1) Ferrando, R.; Jellinek, J.; Johnston, R. L. Nanoalloys: From theory to applications of alloy clusters and nanoparticles. Chem. Rev. (Washington, DC) 2008, 108, 845−910. (2) Gaudry, M.; Cottancin, E.; Pellarin, M.; Lermé, J.; Arnaud, L.; Huntzinger, J. R.; Vialle, J. L.; Broyer, M.; Rousset, J. L.; Treilleux, M.; Mélinon, P. Size and composition dependence in the optical properties of mixed (transition metal/noble metal) embedded clusters. Phys. Rev. B 2003, 67, 155409. (3) Weissker, H.-C.; Mottet, C. Optical properties of pure and coreshell noble-metal nanoclusters from TDDFT: The influence of the atomic structure. Phys. Rev. B 2011, 84, 165443. (4) Logsdail, A. J.; Johnston, R. L. J. Phys. Chem. C 2012, 116, 23616.

5. CONCLUSIONS In this paper we have shown that a variety of icosahedral motifs is possible in AgCu, AgNi, and AgCo nanoalloys. We have considered nanoparticles in a size range (diameters of 3−4 nm) which is rather easily accessible to modern electron microscopy techniques. G



Article

(5) Lima, F. H. B.; de Castro, J. F. R.; Ticianelli, E. A. Silver-cobalt bimetallic particles for oxygen reduction in alkaline media. J. Power Sources 2006, 161, 806−812. (6) Shin, K.; Kim, D. H.; Yeo, S. C.; Lee, H. M. Structural stability of AgCu bimetallic nanoparticles and their application as a catalyst: A DFT study. Catal. Today 2012, 185, 94−98. (7) Kim, S. J.; Stach, E. A.; Handwerker, C. A. Fabrication of conductive interconnects by Ag migration in Cu-Ag core-shell nanoparticles. Appl. Phys. Lett. 2010, 96, 144101. (8) Voyles, P. M.; Muller, D. A.; Grazul, J. L.; Citrin1, P. H.; Gossmann, H.-J. L. Atomic-scale imaging of individual dopant atoms and clusters in highly n-type bulk Si. Nature 2002, 416, 826−829. (9) Cazayous, M.; Langlois, C.; Oikawa, T.; Ricolleau, C.; Sacuto, A. Cu-Ag core-shell nanoparticles: A direct correlation between microRaman and electron microscopy. Phys. Rev. B 2006, 73, 113402. (10) Rossi, G.; Rapallo, A.; Mottet, C.; Fortunelli, A.; Baletto, F.; Ferrando, R. Magic polyicosahedral core-shell clusters. Phys. Rev. Lett. 2004, 93, 105503. (11) Baletto, F.; Mottet, C.; Ferrando, R. Growth of three-shell onionlike bimetallic nanoparticles. Phys. Rev. Lett. 2003, 90, 135504. (12) Janssens, E.; Neukermans, S.; Wang, X.; Veldeman, N.; Silverans, R.; Lievens, P. Stability patterns of transition metal doped silver clusters: Dopant- and size-dependent electron delocalization. Eur. Phys. J. D 2005, 34, 23−27. (13) Mariscal, M. M.; Dassie, S. A.; Leiva, E. P. M. Collision as a way of forming bimetallic nanoclusters of various structures and chemical compositions. J. Chem. Phys. 2005, 123, 184505. (14) Lequien, F.; Creuze, J.; Berthier, F.; Legrand, B. Superficial segregation in nanoparticles: From facets to infinite surfaces. J. Chem. Phys. 2006, 125, 094707. (15) Alcantara-Ortigoza, M.; Rahman, T. S. First principles calculations of the electronic and geometric structure of Ag27Cu7 nanoalloy. Phys. Rev. B 2008, 77, 195404. (16) Delogu, F.; Arca, E.; Mulas, G.; Manai, G.; Shvets, I. Numerical investigation of the stability of Ag-Cu nanorods and nanowires. Phys. Rev. B 2008, 78, 024103. (17) Calvo, F.; Cottancin, E.; Broyer, M. Phys. Rev. B 2008, 77, 121406. (18) Lequien, F.; Creuze, J.; Berthier, F.; Braems, I.; Legrand, B. Superficial segregation, wetting, and dynamical equilibrium in bimetallic clusters: A Monte Carlo study. Phys. Rev. B 2008, 78, 075414. (19) Lequien, F.; Creuze, J.; Berthier, F.; Legrand, B. Dynamical equilibrium in nanoalloys. Faraday Discuss. 2008, 138, 105−117. (20) Langlois, C.; Alloyeau, D.; Bouar, Y. L.; Loiseau, A.; Oikawa, T.; Mottet, C.; Ricolleau, C. Growth and structural properties of CuAg and CoPt bimetallic nanoparticles. Faraday Discuss. 2008, 138, 375− 391. (21) Delfour, L.; Creuze, J.; Legrand, B. Exotic behavior of the outer shell of bimetallic nanoalloys. Phys. Rev. Lett. 2009, 103, 205701. (22) Martinez De La Hoz, J. M.; Tovar, R. C.; Balbuena, P. B. Size effect on the stability of Cu-Ag nanoalloys. Mol. Simul. 2009, 35, 785− 794. (23) Wang, L. L.; Johnson, D. D. Predicted trends of core-shell preferences for 132 late transition-metal binary-alloy nanoparticles. J. Am. Chem. Soc. 2009, 131, 14023−14029. (24) Bochicchio, D.; Ferrando, R. Size-dependent transition to highsymmetry chiral structures in AgCu, AgCo, AgNi, and AuNi nanoalloys. Nano Lett. 2010, 10, 4211−4216. (25) Kilimis, D. A.; Papageorgiou, D. G. Structural and electronic properties of small bimetallic Ag-Cu clusters. Eur. Phys. J. D 2010, 56, 189−197. (26) Nunez, S.; Johnston, R. L. Structures and chemical ordering of small Cu-Ag clusters. J. Phys. Chem. C 2010, 114, 13255−13266. (27) Tang, P. H.; Wu, T. M.; Yen, T. W.; Lai, S. K.; Hsu, P. J. Comparative study of cluster Ag17Cu2 by instantaneous normal mode analysis and by isothermal Brownian-type molecular dynamics simulation. J. Chem. Phys. 2011, 135, 094302.

(28) Molayem, M.; Grigoryan, V. G.; Springborg, M. Theoretical determination of the most stable structures of NimAgn bimetallic nanoalloys. J. Phys. Chem. C 2011, 115, 7179−7192. (29) Molayem, M.; Grigoryan, V. G.; Springborg, M. Global minimum structures and magic clusters of Cum Agn nanoalloys. J. Phys. Chem. C 2011, 115, 22148−22162. (30) Bochicchio, D.; Ferrando, R. Structure and thermal stability of AgCu chiral nanoparticles. Eur. Phys. J. D 2012, 66, 115. (31) Langlois, C.; Li, Z. Y.; Yuan, J.; Alloyeau, D.; Nelayah, J.; Bochicchio, D.; Ferrando, R.; Ricolleau, C. Transition from core-shell to Janus chemical configuration for bimetallic nanoparticles. Nanoscale 2012, 4, 3381−3388. (32) Yildirim, H.; Kara, A.; Rahman, T. S. Tailoring electronic structure through alloying: The AgnCu34−Walesn (n = 0−34) nanoparticle family. J. Phys. Chem. C 2012, 116, 281−291. (33) Xiao, X.-Y. Hcp-icosahedron structural transformation induced by the change in Ag concentration during the freezing of (CoAg)(561) clusters. Chin. Phys. B 2012, 21, 046102. (34) Bochicchio, D.; Ferrando, R. Phys. Rev. B 2013, 87, 165435. (35) Momin, T.; Bhowmick, A. Nanoscale alloying: A study in free Cu−Ag bimetallic clusters. J. Alloys Compd. 2013, 559, 24−33. (36) Mottet, C.; Rossi, G.; Baletto, F.; Ferrando, R. Single impurity effect on the melting of nanoclusters. Phys. Rev. Lett. 2005, 95, 035501. (37) Mackay, A. L. Acta Crystallogr. 1962, 15, 916. (38) Harris, I. A.; Kidwell, R. S.; Northby, J. A. Structure of charged argon clusters formed in a free jet expansion. Phys. Rev. Lett. 1984, 53, 2390. (39) Mottet, C.; Tréglia, G.; Legrand, B. New magic numbers in metallic clusters: an unexpected metal dependence. Surf. Sci. 1997, 383, L719. (40) Lopez-Acevedo, O.; Akola, J.; Whetten, R. L.; Grönbeck, H.; Häkkinen, H. Structure and bonding in the ubiquitous icosahedral metallic gold cluster Au144(SR)60. J. Phys. Chem. C 2009, 113, 5035− 5038. (41) Conway, J. H.; Burgiel, H.; Goodman-Strass, C. The Symmetries of Things; Taylor and Francis Ltd.: New York, 2008. (42) Cyrot-Lackmann, F.; Ducastelle, F. Binding energies of transition-metal atoms adsorbed on a transition metal. Phys. Rev. B 1971, 4, 2406. (43) Rosato, V.; Guillopé, M.; Legrand, B. Thermodynamical and structural properties of f.c.c. transition metals using a simple tightbinding model. Philos. Mag. A 1989, 59, 321. (44) Gupta, R. P. Lattice relaxation at a metal surface. Phys. Rev. B 1981, 23, 6265. (45) Baletto, F.; Mottet, C.; Ferrando, R. Growth simulations of silver shells on copper and palladium nanoclusters. Phys. Rev. B 2002, 66, 155420. (46) Rossi, G.; Schiappelli, G.; Ferrando, R. Formation pathways and energetic stability of icosahedral AgshellCocore nanoclusters. J. Comput. Theor. Nanosci. 2009, 6, 841. (47) Wales, D. J.; Doye, J. P. K. Global optimization by basinhopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J. Phys. Chem. A 1997, 101, 5111−5116. (48) Vitek, V.; Egami, T. Phys. Status Solidi B 1987, 144, 145. (49) www.cp2k.org. (50) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Comput. Phys. Commun. 2005, 167, 103. (51) Lippert, G.; Hutter, J.; Parrinello, M. Theor. Chem. Acc. 1999, 103, 124. (52) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865. (53) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (54) Goedecker, S.; Teter, M.; Hutter, J. Phys. Rev. B 1996, 56, 1703. (55) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys. 2010, 132, 154104. (56) Mortensen, J. J.; Hansen, L. B.; Jacobsen, K. W. Phys. Rev. B 2005, 71, 035109. (57) Enkovaara, J.; et al. J. Phys.: Condens. Matter 2010, 22, 253202. H



Article

(58) Ashcroft, N. W.; Mermin, N. D. Solid State Physics; Holt, Rinehart and Winston: New York, 1976. (59) Bader, R. F. W. Atoms in Molecules - A Quantum Theory; Oxford University Press: Oxford, 1990. (60) Tang, W.; Sanville, E.; Henkelman, G. J. Phys.: Condens. Matter 2009, 21, 084204. (61) theory.cm.utexas.edu/bader/. (62) Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry; Dover Publications Inc.: New York, 1996.

I


Competition between Icosahedral Motifs in AgCu, AgNi, and AgCo

Recommend Documents